# I know the coordinates of several scattered points in space, how can I fit them to a sphere?

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Sterne_17 il 4 Feb 2023
Commentato: Sterne_17 il 4 Feb 2023
I already know the coordinates (x,y,z) of several scattered points on a sphere in space, and my goal is to fit a sphere and get the radius. I think I just need to bring their coordinates into the code I found. I would like to ask how to bring in the coordinates of these points?
function [r,a,b,c] = sphereFit(data)
xx = data(:,1);
yy = data(:,2);
zz = data(:,3);
AA = [-2*xx, -2*yy , -2*zz , ones(size(xx))];
BB = [ -(xx.^2+yy.^2+zz.^2)];
YY = mldivide(AA,BB); %Trying to solve AA*YY = BB
a = YY(1);
b = YY(2);
c = YY(3);
D = YY(4); % D^2 = a^2 + b^2 + c^2 -r^2(where a,b,c are centers)
r = sqrt((a^2+b^2+c^2)-D);
The second code:
A=[mean(X(:,1).*(X(:,1)-mean(X(:,1)))), ...
2*mean(X(:,1).*(X(:,2)-mean(X(:,2)))), ...
2*mean(X(:,1).*(X(:,3)-mean(X(:,3)))); ...
0, ...
mean(X(:,2).*(X(:,2)-mean(X(:,2)))), ...
2*mean(X(:,2).*(X(:,3)-mean(X(:,3)))); ...
0, ...
0, ...
mean(X(:,3).*(X(:,3)-mean(X(:,3))))];
A=A+A.';
B=[mean((X(:,1).^2+X(:,2).^2+X(:,3).^2).*(X(:,1)-mean(X(:,1))));...
mean((X(:,1).^2+X(:,2).^2+X(:,3).^2).*(X(:,2)-mean(X(:,2))));...
mean((X(:,1).^2+X(:,2).^2+X(:,3).^2).*(X(:,3)-mean(X(:,3))))];
Center=(A\B).';
Which code should I choose and apply correctly?
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John D'Errico il 4 Feb 2023
Modificato: John D'Errico il 4 Feb 2023
So, instead of using the code I already gave you that fits the sphere in a well posed way in your last question, now you ask which of these poorly written pieces of code you should use. Sigh. If someone does tell you which poorly written code to use, will you then turn the question into an image processing question again?
Sterne_17 il 4 Feb 2023

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### Risposta accettata

Image Analyst il 4 Feb 2023
Modificato: Image Analyst il 4 Feb 2023
It looks like the input data for both functions is an N-by-3 matrix.
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